Problem: Solve for $x$ : $x^2 - 4x - 5 = 0$
The coefficient on the $x$ term is $-4$ and the constant term is $-5$ , so we need to find two numbers that add up to $-4$ and multiply to $-5$ The two numbers $1$ and $-5$ satisfy both conditions: $ {1} + {-5} = {-4} $ $ {1} \times {-5} = {-5} $ $(x + {1}) (x {-5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 1) (x -5) = 0$ $x + 1 = 0$ or $x - 5 = 0$ Thus, $x = -1$ and $x = 5$ are the solutions.